THERMODYNAMICS OF FLUIDS. 19 



diagrams in which x = logv and y = logp, or in which x r\ and 

 2/ = log; but the diagrams formed by these methods will evidently 

 be radically different from one another. It is to be observed that 

 each of these methods is what may be called a method of definite scale 

 for work and heat ; that is, the value of y in any part of the diagram 

 is independent of the properties of the fluid considered. In the first 



method y = -^- , in the second y = . In this respect these methods 



. 



have an advantage over many others. For example, if we should 

 make x = log v, y = r\ y the value of y in any part of the diagram would 

 depend upon the properties of the fluid, and would probably not vary 

 in any case, except that of a perfect gas, according to any simple law. 

 The conveniences of the entropy-temperature method will be found 

 to belong in nearly the same degree to the method in which the 

 co-ordinates are equal to the entropy and the logarithm of the tem- 

 perature. No serious difficulty attaches to the estimation of heat and 

 work in a diagram formed on the latter method on account of the 

 variation of the scale on which they are represented, as this variation 

 follows so simple a law. It may often be of use to remember that 

 such a diagram may be reduced to an entropy-temperature diagram 

 by a vertical compression or extension, such 

 that the distances of the isothermals shall be 

 made proportional to their differences of tem- 

 perature. Thus if we wish to estimate the work 

 or heat of the circuit ABCD (fig. 7), we may 

 draw a number of equidistant ordinates (isen- A 

 tropics) as if to estimate the included area, and 

 for each of the ordinates take the differences 

 of temperature of the points where it cuts the 

 circuit; these differences of temperature will 

 be equal to the lengths of the segments made by the corresponding 

 circuit in the entropy-temperature diagram upon a corresponding 

 system of equidistant ordinates, and may be used to calculate the 

 area of the circuit in the entropy-temperature diagram, i.e., to find 

 the work or heat required. We may find the work of any path by 

 applying the same process to the circuit formed by the path, the iso- 

 metric of the final state, the line of no pressure (or any isopiestic ; see 

 note on page 9), and the isometric of the initial state. And we may 

 find the heat of any path by applying the same process to a circuit 

 formed by the path, the ordinates of the extreme points and the line 

 of absolute cold. That this line is at an infinite distance occasions no 

 difficulty. The lengths of the ordinates in the entropy-temperature 

 diagram which we desire are given by the temperature of points in 

 the path determined (in either diagram) by equidistant ordinates. 



